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Author: J D Renton
Publisher: Elsevier
ISBN: 0857099582
Category : Science
Languages : en
Pages : 212
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Book Description
This updated version covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987. It emphasises 3-dimensional elasticity, concisely covering this important subject studied in most universities by filling the gap between a mathematical and the engineering approach. Based on the author's extensive research experience, it reflects the need for more sophisticated methods of elastic analysis than is usually taught at undergraduate level. The subject is presented at the level of sophistication for engineers with mathematical knowledge and those familiar with matrices. Readers wary of tensor notation will find help in the opening chapter. As his text progresses, the author uses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis. Relatively inaccessible material with important applications receives special attention, e.g. Russian work on anisotropic materials, the technique of thermal imaging of strain, and an analysis of the San Andreas fault. Tensor equations are given in straightforward notation to provide a physical grounding and assist comprehension, and there are useful tables for the solution of problems. Covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987 Emphasises 3-dimensional elasticity and fills the gap between a mathematical and engineering approach Uses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis
Author: J D Renton
Publisher: Elsevier
ISBN: 0857099582
Category : Science
Languages : en
Pages : 212
Get Book
Book Description
This updated version covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987. It emphasises 3-dimensional elasticity, concisely covering this important subject studied in most universities by filling the gap between a mathematical and the engineering approach. Based on the author's extensive research experience, it reflects the need for more sophisticated methods of elastic analysis than is usually taught at undergraduate level. The subject is presented at the level of sophistication for engineers with mathematical knowledge and those familiar with matrices. Readers wary of tensor notation will find help in the opening chapter. As his text progresses, the author uses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis. Relatively inaccessible material with important applications receives special attention, e.g. Russian work on anisotropic materials, the technique of thermal imaging of strain, and an analysis of the San Andreas fault. Tensor equations are given in straightforward notation to provide a physical grounding and assist comprehension, and there are useful tables for the solution of problems. Covers the considerable work on research and development to determine elastic properties of materials undertaken since the first edition of 1987 Emphasises 3-dimensional elasticity and fills the gap between a mathematical and engineering approach Uses Cartesian tensors to develop the theory of thermoelasticity, the theory of generalised plane stress, and complex variable analysis
Author: John A. Eisele
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Author: John A. Eisele
Publisher: John Wiley & Sons
ISBN:
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Author: A. I. Borisenko
Publisher: Courier Corporation
ISBN: 0486131904
Category : Mathematics
Languages : en
Pages : 288
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Book Description
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
Author: C. E. Springer
Publisher: Courier Corporation
ISBN: 048632091X
Category : Mathematics
Languages : en
Pages : 256
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Book Description
Assuming only a knowledge of basic calculus, this text's elementary development of tensor theory focuses on concepts related to vector analysis. The book also forms an introduction to metric differential geometry. 1962 edition.
Author: Liqun Qi
Publisher: SIAM
ISBN: 1611974747
Category : Mathematics
Languages : en
Pages : 313
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Book Description
Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors. ?
Author: Xian-Da Zhang
Publisher: Cambridge University Press
ISBN: 1108417418
Category : Computers
Languages : en
Pages : 761
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Book Description
The theory, methods and applications of matrix analysis are presented here in a novel theoretical framework.
Author: Mikhail Itskov
Publisher: Springer Science & Business Media
ISBN: 3540939075
Category : Technology & Engineering
Languages : en
Pages : 253
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Book Description
There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.
Author: Toshio Sakata
Publisher: Springer
ISBN: 4431553878
Category : Computers
Languages : en
Pages : 136
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Book Description
This book provides comprehensive reviews of recent progress in matrix variate and tensor variate data analysis from applied points of view. Matrix and tensor approaches for data analysis are known to be extremely useful for recently emerging complex and high-dimensional data in various applied fields. The reviews contained herein cover recent applications of these methods in psychology (Chap. 1), audio signals (Chap. 2) , image analysis from tensor principal component analysis (Chap. 3), and image analysis from decomposition (Chap. 4), and genetic data (Chap. 5) . Readers will be able to understand the present status of these techniques as applicable to their own fields. In Chapter 5 especially, a theory of tensor normal distributions, which is a basic in statistical inference, is developed, and multi-way regression, classification, clustering, and principal component analysis are exemplified under tensor normal distributions. Chapter 6 treats one-sided tests under matrix variate and tensor variate normal distributions, whose theory under multivariate normal distributions has been a popular topic in statistics since the books of Barlow et al. (1972) and Robertson et al. (1988). Chapters 1, 5, and 6 distinguish this book from ordinary engineering books on these topics.
Author: Aleksandr Ivanovich Borisenko
Publisher: Courier Corporation
ISBN: 9780486638331
Category : Mathematics
Languages : en
Pages : 292
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Book Description
Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.
